On simplified spherical harmonics equations for the radiative transfer equation

Abstract

The radiative transfer equation (RTE) arises in a wide range of applications in sciences and engineering. Due to the high dimension and complicated form of the RTE, it is challenging to solve the equation directly. In the literature, several approximation methods were developed for the RTE. One approximation method, the simplified spherical harmonics (SP N ) method, provides an efficient way to generate good approximate solutions of the RTE with high absorption and small geometries. The main purpose of the paper is to study well-posedness of the simplified spherical harmonics system. The weak formulation used in the proof of the solution existence and uniqueness provides a starting point for developing the Galerkin finite element method to solve the simplified spherical harmonics system.